Dynamic scaling approach to glass formation

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Abstract

Experimental data for the temperature dependence of relaxation times are used to argue that the dynamic scaling form, with relaxation time diverging at the critical temperature [Formula Presented] as [Formula Presented] is superior to the classical Vogel form. This observation leads us to propose that glass formation can be described by a simple mean-field limit of a phase transition. The order parameter is the fraction of all space that has sufficient free volume to allow substantial motion, and grows logarithmically above [Formula Presented] Diffusion of this free volume creates random walk clusters that have cooperatively rearranged. We show that the distribution of cooperatively moving clusters must have a Fisher exponent [Formula Presented] Dynamic scaling predicts a power law for the relaxation modulus [Formula Presented] where z is the dynamic critical exponent relating the relaxation time of a cluster to its size. Andrade creep, universally observed for all glass-forming materials, suggests [Formula Presented] Experimental data on the temperature dependence of viscosity and relaxation time of glass-forming liquids suggest that the exponent ν describing the correlation length divergence in this simple scaling picture is not always universal. Polymers appear to universally have [Formula Presented] (making [Formula Presented] However, other glass-formers have unphysically large values of [Formula Presented] suggesting that the availability of free volume is a necessary, but not sufficient, condition for motion in these liquids. Such considerations lead us to assert that [Formula Presented] is in fact universal for all glass- forming liquids, but an energetic barrier to motion must also be overcome for strong glasses.

Original languageEnglish (US)
Pages (from-to)1783-1792
Number of pages10
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume61
Issue number2
DOIs
StatePublished - Jan 1 2000

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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